How dynamic adsorption controls surfactant-enhanced boiling

Improving boiling is challenging due to the unpredictable nature of bubbles. One way to enhance boiling is with surfactants, which alter the solid–liquid and liquid–vapor interfaces. The conventional wisdom established by previous studies suggests that heat transfer enhancement is optimized near the critical micelle concentration (CMC), which is an equilibrium property that depends on surfactant type. However, these studies only tested a limited number of surfactants over small concentration ranges. Here, we test a larger variety of nonionic and anionic surfactants over the widest concentration range and find that a universal, optimal concentration range exists, irrespective of CMC. To explain this, we show that surfactant-enhanced boiling is controlled by two competing phenomena: (1) the dynamic adsorption of surfactants to the interfaces and (2) the increase in liquid dynamic viscosity at very high surfactant concentrations. This dynamic adsorption is time-limited by the millisecond-lifetime of bubbles on the boiling surface—much shorter than the timescales required to see equilibrium behaviors such as CMC. At very high concentrations, increased viscosity inhibits rapid bubble growth, reducing heat transfer. We combine the effects of adsorption and viscosity through a simple proportionality, providing a succinct and useful understanding of this enhancement behavior for boiling applications.


FIG. S.2. The heat flux as a function of the wall superheat.
To ensure all bubble nucleation sites were activated on the heating surface 1 , we record heat flux-averaged descending boiling curves (heat flux range: 50-1 W/cm 2 & sample range: 1 sample every 2 W/cm 2 ) under saturation conditions (fluid temperature ~ 98 ℃ and atmospheric pressure ~ 1 atm). The boiling experiments reveal that regardless of the type of the surfactant, plots (a), (b), (c), (d), and (e) show a decrease in the wall superheat as the molar concentration, c, increases. This trend continues up to a concentration range of c ~ 1-3.5 mol/m 3 , which enhances the HTC. Above this range c > 1-3.5 mol/m 3 , the wall superheat ramps back up to higher temperature values exacerbating the HTC.

FIG. S.3. Custom viscometer setup.
We recorded videos at a set frame rate of 120 FPS using (a) a camera positioned far away from the viscometer. (b) The viscometer consists of 3D printed resin parts, a rectangular borosilicate glass enclosure, a light source on the back of the glass container to provide enough illumination, a thermocouple for temperature measures of the fluid, and a magnetic stir bar to mix the aqueous solution of surfactant in the fluid. We use a micropipette to add/remove aqueous solution through a small orifice on the top plate to reach the desired concentration value. For viscosity measurements, we use (c) the falling sphere (stainless steel bearing balls) method. Experiments are conducted at a room temperature of 24~25 ℃. We use an image processing technique to estimate the velocity of the ball bearing in a set region (pink rectangle) using Wolfram Mathematica. A custom 3D printed ruler is used for pixel calibration and estimate the distance traveled by the ball bearing in the set region. Then, we estimate the viscosity of the fluid based on the recorded velocity values.

FIG. S.4. Results of viscosity tests.
Experiment tests conducted at room temperature conditions (24~25℃). At a relatively low molar concentration, both surfactants, S12S and TW40, show minor changes in the viscosity. As we increase the mass concentration of surfactant, both aqueous solutions become more viscous, with an apparent increase in viscosity when c > 1 mol/m 3 . A small dip in viscosity from 0.01 to 1 g/L is likely due to measurement error and drifting temperature conditions in the laboratory.

FIG. S.5. Dynamic contact angle measurement.
The averaged dynamic contact angles before and after testing show that the experimental sample (copper tube) did not exhibit a significant change in wettability. These contact angle tests of DI water droplets were conducted at room temperature conditions (≈23 °C) using a custom-built goniometer.    Fig. S.2). The departure diameter, d , is proportional to some function of the Jakob Number, Ja , which is Here, is the surface tension, is the gravitational acceleration, l and v are the densities of the liquid and vapor, respectively, p is the specific heat at constant pressure, and ℎ fg is the specific latent heat of vaporization.
Solving for the bubble departure diameter with typical properties in boiling water, we find d = 1.95 ± 0.21 mm. Then, we refer to Cole's equation (25)

S.2. Characteristic timescale of diffusion
Most surfactants follow 7 the non-linear Langmuir isotherm, defined as where Γ eq is the equilibrium surface concentration, Γ max is the maximum surface concentration (a theoretical limit 7 ), L is the Langmuir equilibrium adsorption constant, and is bulk concentration. where the surface tension would be very near the value of pure water.
where is the surface tension of the surfactant-free interface, and is the product of the ideal gas constant and the temperature of the fluid. Solving for with dynamic adsorption properties of TW40 in water at room temperature (23 − 25 ℃), we get a drop in surface tension of 3.42 ± 0.02 mN/m.

S.3. Dimensionless Ward-Tordai equation
In this work, we solve the classic Ward-Tordai equation 9 Here, is a dummy variable and 0 is the subsurface concentration.  developed by Li 10 . We replicated this algorithm in Mathematica with the following code.